REFERENCES & NOTES

¹ Iamblichus, De Communi Mathematica Scientia Libebr, 69,26-29. Edited by N. Festa, 1891;
Edited with additions & corrections by U. Klein, Stuttgart: Teubner, 1975) [Return to text]
² Gregory Shaw, Theurgy and the Soul: The Neoplatonism of Iamblichus,
The Pennsylvania State University Press, University Park, PA, 1995 [Return to text]
³ Proclus, In Euclkidem 141; cited by J. Trouillard, "La Puissance secrete du nombre chez Proclos,"
Revue de Philosophie Ancienne 1 (1983):234 [Return to text]
⁴ Paget Toynbee, "Dante's References to Pythagoras" in Romania (1895) 376-384 [Return to text]
⁵ Richard H. Lansing (trans.), Dante's Il Convivio: The Banquet, Garland Publishing, NY (1990) [Return to text]
⁶ "Minor Works of Dante (Opere Minore)" (www.princeton.edu/~batke/dante/minor/) [Return to text]
⁷ Richard H. Lansing (trans.), Dante's Il Convivio: The Banquet,
(http://dante.ilt.columbia.edu/books/convivi/index.html) [Return to text]
⁸ Prue Shaw, Dante, Monarchia, Cambridge University Press (1995). Dante's Monarchia in Latin is available
at George Mason University (www.gmu.edu/departments/fld/CLASSICS/dante.mon1.html) [Return to text]
⁹ Vincent Foster Hopper, Medieval Number Symbolism, Copper Square Publishers, NY (1969), p. 142.
In footnote 39 to Dante's Il Convivio, Richard Lansing writes: “ Rome was founded, according to tradition,
on 21 April 753 B.C. For the references see Orosius, Historiarum adversus paganos libri septem VII, 3 and
Livy, History of Rome I, 18, a passage which Dante either did not read carefully or misremembered, since it
explicitly discredits the notion that Pythagoras lived in the time of Numa Pompilius (717-673 B.C.) [Return to text]
¹⁰ John Dillon & Jackson Hershbell (ed.), Iamblichus, On the Pythagorean Way of Life,
Scholars Press, Atlanta (1991), p. 53 [Return to text]
¹¹ John Dillon & Jackson Hershbell, Op. Cit., pp. 33-34 [Return to text]
¹² John Dillon & Jackson Hershbell, Op. Cit., pp. 77, 113 [Return to text]
¹³ John Dillon & Jackson Hershbell, Op. Cit., pp. 127-129 [Return to text]
¹⁴ Porphyry, Life of Pythagoras: “What he said to his disciples, no man can tell for certain, for they preserved an
exceptional silence.” [quoted in Christopher Bamford (ed.), Homage to Pythagoras: Rediscovering Sacred Science,
Lindisfarne Press, Hudson, NY (1994), p. 9. [Return to text]
¹⁵ Ernest Hatch Wilkins, Thomas G. Bergin, & Anthony J. De Vito, A Concordance to the Divine Commedy
Harvard University Press, Cambridge, MA (1966) [Return to text]
¹⁶ Dante, Epistle to Can Grande translated by James Marchand
(gopher://ccat.sas.upenn.edu:70/00/journals/Recentiores/Dante/Cangrande.English) [Return to text]
¹⁷ Allen Mandelbaum (trans.), Dante, Paradiso, Bantam Books, NY (1986), p. 303. [Return to text]
¹⁸ Paget Toynbee, A Life of Dante, 3rd Ed., Methuen, London (1904), p. 113. [Return to text]
¹⁹ Christopher McIntosh, The Astrologers and their Creed: an historical outline,
Hutchinson of London, 1969, pp. 67-69 [Return to text]
²⁰ James Trager, The People's Chronology, Holt, Rinehart and Winston, NY (1979), pp. 141, 159, 207. [Return to text]
²¹ Paget Toynbee, Dante Dictionary, Clarendon Press, Oxford (1898) [Return to text]
²² Allen Mandelbaum (trans.), Dante, Paradiso, Bantam Books, NY (1986), p.301. [Return to text]
²³ Raymond Klibansky, The Continuity of the Platonic Tradition during the Middle Ages,
The Warburg Institute, London (1939), pp. 29, 284. [Return to text]
²⁴ Frances M. Cornford, Plato's Cosmology (The Timaeus of Plato translated with a running commentary)
Routledge & Kegan Paul, London (1937), p. 67 [Return to text]
²⁵ A. E. Taylor, A Commentary on Plato's Timaeus, Clarendon Press, Oxford (1928), p. 137 [Return to text]
²⁶ R. D. Archer-Hind, The Timaeus of Plato, Macmillan, London (1888), p. 107 [Return to text]
²⁷ J. Cook Wilson, On the Interpretation of Plato's Timaeus, David Nutt, London (1889)
(Garland Publishing, NY, 1980 reprint), p. 10 [Return to text]
²⁸ R. G. Bury, Plato: Timaeus, Harvard University Press, Cambridge (1952), p. 66 [Return to text]
²⁹ Paul Friedländer, Plato 3: The Dialogues (trans. from the German by Hans Meyerhoff)
Bollingen Series LIX, Princeton University Press (1969), p. 367 [Return to text]
³⁰ Joh Wrobel, Platonis Timaeus: Interprete Chalcidio Cum Eiusden Commentario, Teubneri, Leipzig (1876)
(reprint, Minerva GMBH, Frankfurt, 1963), p. 32 & Figure 7 (Crantor's diagram) [Return to text]
³¹ John Sallis, Chorology: On Beginning in Plato's Timaeus,
Indiana University Press, Bloomington (1999), p. 71 [Return to text]
³² George S. Claghorn, Aritstotle Criticism of Plato's Timaeus, Martinus Nijhoff, The Hague (1954) [Return to text]
³³ Iamblichus, The Theology of Arithmetic (translated by Robin Waterfield),
Phane Press, Grand Rapids, MI (1988), pp. 13-21 [Return to text]
³⁴ Benjamin Jowett (trans.) Plato's Timaeus, in Edith Hamilton & Huntington Cairns,
Collected Dialogues of Plato, Bollingen Series LXXI, Princeton University Press, 1961, p. 1165 [Return to text]
³⁵ Thomas Taylor (trans.) Plato: The Timaeus and The Critias (forward by R. Catesby Taliaferro),
Bollingen Series, Pantheon Books, NY, 1944, p. 123 (original edition 1804) [Return to text]
³⁶ Proclus Diadochus, Commentaries on the Timaeus of Plato (translated by Thomas Taylor),
A. J. Valpy, London (1820), Bk III, p. 58 [Return to text]
³⁷ Lou Brisson & F. Walter Meyerstein, Inventing the Universe: Plato's Timaeus, The Big Bang, and the Problem of
Scientific Knowledge State University Press of New York Press, Albany (1995), pp. 32-39 [Return to text]
³⁸ Anne Freire Ashbaugh, Plato's Theory of Explanation: A Study of the Cosmological Account in the Timaeus,
State University Press of New York Press, Albany (1988), pp. 22-29 [Return to text]
³⁹ Annemarie Schimmel, The Mystery of Numbers, Oxford University Press, NY (1993), p. 237 [Return to text]
⁴⁰ John Macqueen, Numerology, Edinburgh University Press, Edinburgh (1985), pp. 26-46 [Return to text]
⁴¹ Christopher Butler, Number Symbolism, Routledge & Kegan Paul, London (1970), pp. 1-19 [Return to text]
⁴² Ronald H. Isaacs, The Jewish Book of Numbers, Jason Aronson Inc., Northvale, NJ (1996) [Return to text]
⁴³ Michael J. B. Allen, Nuptial Arithmetic: Marsilio Ficino's Commentary on the Fatal Number
in Book VIII of Plato's Republic, University of California Press, Berkeley (1994), pp. 8, 35, 46 [Return to text]
⁴⁴ Manfred Hardt, Die Zahl in der Divina Commedia, Athenaum Verlag, Frankfurt (1973) [Return to text]
⁴⁵ John J. Guzzardo, Dante: Numerological Studies, Peter Lang, NY (1987) [Return to text]
⁴⁶ King Wên & Duke of Chou, I Ching: Book of Changes, Bk II.9.1-2,
Richard Wilhelm & Cary F. Baynes (trans.),
Bollingen Series XIX, Princeton University Press (1961), pp. 308-310 [Return to text]
⁴⁷ I Ching, Op. Cit., Hexagram 55, p. 213 [Return to text]
⁴⁸ Hopper, Op. Cit., (ref. 9) p. 42 [Return to text]
⁴⁹ Butler, Op. Cit., (ref. 41) p. 2 [Return to text]
⁵⁰ Charles-Albert Reichen, A History of Astronomy, Hawthorn, NY (1961), p. 15 [Return to text]
⁵¹ Aristotle, Metaphysics, 1074a6 (Bk XII or Book Lambda)
W. D. Ross (trans.), Clarendon Press, Oxford (1924)
in Jonathan Barnes (ed.), The Complete Works of Aristotle,
Vol. 2, Bollingen Series LXXI.2, Princeton University Press (1984), p. 1697 [Return to text]
⁴⁰ Ron Knott, "Fibonacci Numbers and Nature" (www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html)
[Return to text]
⁵³ Thomas Taylor, 55 Dialogues of Plato, A. J. Valpy, London (1804) [Return to text]
⁵⁴ Isidore Kozminsky, Numbers: Their Meaning and Magic, Rider, London (1912), p. 51 [Return to text]
⁵⁵ Peter Y. Chou, "On the Number 55" (www.wisdomportal.com/Numbers/55.html) [Return to text]
⁵⁶ Science News, Vol. 129 (January 11, 1986), p. 20 [Return to text]
⁵⁷ Donald K. Yeomans, The Comet Halley Handbook, NASA (May 15, 1983), p. 20 [Return to text]
⁵⁸ Wilkins, Op. Cit., (ref. 15), pp. 544-545 [Return to text]
⁵⁹ Edward Allen Fay, Concordance of the Divina Commedia
Little, Brown & Co., Boston (1888), pp. 688-689 [Return to text]
⁶⁰ Luciano Lovera, Rosanna Bettarini, Anna Mazzarello, & Francesco Mazzoni,
Concordanza della Commedia di Dante Alighieri,
Guilio Einaudi editore, Torino, Italy (1975), Vol. III, pp. 2311-2313 [Return to text]
⁶¹ William A. Williams, Jr. (Web Search Program)
Concordance: Dante's Divine Comedy (www.concordance.com/dante.htm) (1998) [Return to text]
⁶² Charles Singleton, "The Poet's Number at the Center," MLN 80 (1965) 1-10 [Return to text]
⁶³ J. L. Logan, "The Poet's Central Numbers," MLN 86 (1965) 95-98 [Return to text]
⁶⁴ Betty Vanderwielen, "The Significance of Numbers in the Structuring of Dante's Commedia," in
Robert L. Surles, Medieval Numerology: A Book of Essays (1993), pp. 77-91 [Return to text]
⁶⁴ Wilkins, Op. Cit. (ref. 15), p. 591 [Return to text]
⁶⁶ Charles Singleton (trans.), Dante, Purgatorio, Bollingen Series LXXX,
Princeton University Press (1973), p. 25 [Return to text]
⁶⁷ Singleton, Op. Cit., p. 91 [Return to text]
⁶⁸ Mandelbaum, Op. Cit., (ref. 17), pp. 121, 221, 303. [Return to text]
⁶⁹ Digital Dante at Columbia University (http://dante.ilt.columbia.edu/new/comedy/index.html) [Return to text]
⁷⁰ M. A. Orr, Dante and the Early Astronomers, Gall & Inglis, London (1913),
Reprint edition, Allan Wingate, London (1956), pp. 235-288. [Return to text]
⁷¹ Richard Kay, Dante's Christian Astrology, University of Pennsylvania Press, Philadelphia (1994) [Return to text]
⁷² Hsiang-shan ch'üan-chi (Complete Works of Lu Hsiang-shan) 22.5a in
Wing-tsit Chan (ed.), A Source Book in Chinese Philosophy,
Princeton University Press (1963), p. 579 [Return to text]
⁷³ Joseph Gallagher, To Hell & Back with Dante, Triumph Books, Liquori, MO (1996), p. 82 [Return to text]
⁷⁴ John Ciardi (trans.), Dante: The Divine Comedy, Norton, NY (1977), pp. 12, 236 [Return to text]
⁷⁵ John Freccero, The Poetics of Conversion, Harvard University Press, Cambridge (1986), pp. 174, 176 [Return to text]
⁷⁶ Dante, La Vita Nuova (trans. Barbara Reynolds), Penguin Books, Baltimore (1969), pp. 80-81 [Return to text]
⁷⁷ Wilkins, Op. Cit., (ref. 15), p. 145 [Return to text]
⁷⁸ Singleton, Op. Cit., (ref. 66), p. 742 [Return to text]
⁷⁹ Lansing, Op. Cit., (ref. 5), p. 6 [Return to text]
⁸⁰ George Ifrah, From One to Zero: A Universal History of Numbers, Penguin Books, (1987), p. 261 [Return to text]
⁸¹ Werner Jaeger, Early Christianity and Greek Paideia,
Harvard University Press, Cambridge, MA (1961) [Return to text]
⁸² Freccero, Op. Cit., (ref. 75), pp. 180-185 [Return to text]
⁸³ Freccero, Op. Cit., (ref. 75), p. 262 [Return to text]